Here is the full list of all 37 Rebel Galaxy achievements. It takes around 50-60 hours to unlock all of the achievements on Windows.
Reach rank 5 in any Guild
Woke Trell
Purchase a new ship
Join the Merchant's Guild
Trade with a Merchant while in flight
Hire a mercenary
Hack 10 transponders successfully
Destroy 250 Fighter-Class Craft
Destroy 2,500 Fighter-Class Craft
Destroy 100 Capital-Class Craft
Destroy 1,000 Capital-Class Craft
Reach a Net Worth of 5 Million Credits
Reach a Net Worth of 50 Million Credits
Complete the main campaign
Jump out of the first solar system
Shoot down 500 torpedoes
Complete 50 missions from the mission board
Salvage 50 Containers
Gather 200 objects with a tractor beam
Pirate a merchant
Mine 50 asteroids using a Fault Tracker
Collect 10 bounties
Collect 100 bounties
Kill 1 Pirate Lord
Kill 20 Pirate Lords
Join the Mercenaries' Guild
Rescue 20 merchants
Successfully bribe a Militia official
Become neutral to pirate factions
Become friendly to the Militia
Find a Progenitor Shard
Find the Face of Gozu
Find an Antimatter Speck
Break 1 blockade
Break 10 blockades
Purchase a Destroyer-class ship
Purchase a Dreadnaught-class ship